AI Feynman: A physics-inspired method for symbolic regression

By S. Udrescu, Max Tegmark. Science Advances, 2019

1,284 citations recorded by the source corpus.

Our physics-inspired algorithm for symbolic regression is able to discover complex physics equations from mere tables of numbers. A core challenge for both physics and artificial intelligence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality, and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult physics-based test set, we improve the state-of-the-art success rate from 15 to 90%.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/3e9af4289e4bbd3fb912a68ac8430fd2d9a8ab4d

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In Artificial Intelligence

Citations in the corpus

Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, methodology): “[270] design a recursive multidimensional version of symbolic regression that uses a NN in conjunction with techniques from physics to narrow the search space.”
KAN: Kolmogorov-Arnold Networks (2024, neutral): “There are many off-the-shelf symbolic regression methods based on genetic algorithms (Eureka [73], GPLearn [74], PySR [75]), neural-network based methods (EQL [76], OccamNet [77]), physics-inspired method (AI Feynman [20, 21]), and reinforcement learning-based methods [78].”
Contemporary Symbolic Regression Methods and their Relative Performance (2021, methodology): “Udrescu and Tegmark [18] describe each dataset as containing 10 5 rows, but each actually contains 10 6 .”
On scientific understanding with artificial intelligence (2022, methodology): “[23] Silviu-Marian Udrescu and Max Tegmark, “Ai feynman: A physics-inspired method for symbolic regression,” Science Advances 6, eaay2631 (2020).”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, methodology): “Udrescu et al. [251] designs a recursive multidimensional version of symbolic regression that uses a NN in conjunction with techniques from physics to narrow the search space.”
Interpretable scientific discovery with symbolic regression: a review (2022, positive): “More recently, SR has been addressed with deep learning-based methods [27, 28, 19, 29, 30, 31, 32, 33] which leverage neural networks (NNs) to learn accurate symbolic models.”
End-to-end symbolic regression with transformers (2022, positive): “Pareto plot comparing the average test performance and inference time of our models with baselines provided by the SRbench benchmark [7], both on Feynman SR problems [1] and black-box regression problems.”
Discovering Symbolic Models from Deep Learning with Inductive Biases (2020, background): “There are many other alternative approaches to eureqa, including [25, 26, 27, 28, 29, 30].”
Solving Inverse Problems in Stochastic Self-Organising Systems through Invariant Representations (2025, unknown): “A future avenue will be to combine the method with modern symbolic regression techniques [54, 56] to recover the functional forms of the underlying models, and evaluate the method when searching in state space.”